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Find the coordinates of the… (Class 12 Maths 2023, Q30a)

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MathsCBSE Class 12 · Board exam 2023, set 65/5/1 · 3 marks · Short answer

CBSE Class 12 Mathematics 2023: question 30(a)

Set in the CBSE Class 12 board exam of 2023, paper 65/5/1, section C, question 30(a), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q30(a) · 3 marks · Short answerThree Dimensional Geometry

Find the coordinates of the foot of the perpendicular drawn from the point P(0, 2, 3) to the line .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 65/5/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Write any point on the line in terms of a parameter .

Hint 2

The vector from P to that point must be perpendicular to the line's direction , so their dot product is zero.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

  1. A general point on the line is .

    Direction ratios of are .

    1 mark

  2. Since the line (direction ratios ):

    , so

    1 mark

  3. Foot of the perpendicular:

    1 mark

Answer: (2, 3, −1)

Where the marks are

  • Writes the general point and direction ratios of PM (1 mark)
  • Uses the perpendicularity condition to get (1 mark)
  • Foot of perpendicular is (1 mark)

Revise the chapter

Practise this chapterBoard-style questions from Three Dimensional Geometry, one at a time, marked against the answer key and marking points.Back to the full paper2023 board paper, set 65/5/1: every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.